Space of modular forms of level 2340, weight 2, and Character 2340.bp

• Label: 2340.2.bp
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.bp
• Rep. character: $\chi_{2340}(1477,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $70$
• Newform subspaces: $9$
• Sturm bound: $1008$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.bp (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1008\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

	Total	New	Old
Modular forms	1056	70	986
Cusp forms	960	70	890
Eisenstein series	96	0	96

Trace form

70 * q + 2 * q^5 - 8 * q^11 - 6 * q^13 - 2 * q^17 + 4 * q^19 - 20 * q^23 + 6 * q^25 - 12 * q^35 - 12 * q^37 - 14 * q^41 - 4 * q^43 - 8 * q^47 + 54 * q^49 - 18 * q^53 + 4 * q^55 - 16 * q^61 - 22 * q^65 + 4 * q^71 - 8 * q^77 + 80 * q^83 + 2 * q^85 - 18 * q^89 + 36 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2340.2.bp.a	$2340$	$2$	2340.bp	65.f	$4$	$2$	$1$	$18.685$	\(\Q(\sqrt{-1}) \)	None		✓			2340.2.u.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-2)q^{5}-4 q^{7}+(-2 i+2)q^{11}+\cdots\)
2340.2.bp.b	$2340$	$2$	2340.bp	65.f	$4$	$2$	$1$	$18.685$	\(\Q(\sqrt{-1}) \)	None					260.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-2)q^{5}+4 q^{7}+(-4 i+4)q^{11}+\cdots\)
2340.2.bp.c	$2340$	$2$	2340.bp	65.f	$4$	$2$	$1$	$18.685$	\(\Q(\sqrt{-1}) \)	None		✓			2340.2.u.a	$2$	$1$	\(0\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+2)q^{5}-4 q^{7}+(2 i-2)q^{11}+\cdots\)
2340.2.bp.d	$2340$	$2$	2340.bp	65.f	$4$	$4$	$2$	$18.685$	\(\Q(\zeta_{8})\)	None		✓			2340.2.u.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}+\zeta_{8}^{3})q^{5}-3q^{7}-\zeta_{8}q^{11}+\cdots\)
2340.2.bp.e	$2340$	$2$	2340.bp	65.f	$4$	$4$	$2$	$18.685$	\(\Q(i, \sqrt{5})\)	None					260.2.m.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2}+\beta _{3})q^{11}+\cdots\)
2340.2.bp.f	$2340$	$2$	2340.bp	65.f	$4$	$4$	$2$	$18.685$	\(\Q(\zeta_{8})\)	None		✓			2340.2.u.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+3q^{7}+\zeta_{8}q^{11}+\cdots\)
2340.2.bp.g	$2340$	$2$	2340.bp	65.f	$4$	$8$	$4$	$18.685$	8.0.\(\cdots\).2	None					260.2.m.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{3}+\beta _{7})q^{5}+(-1-\beta _{2})q^{7}+(-2+\cdots)q^{11}+\cdots\)
2340.2.bp.h	$2340$	$2$	2340.bp	65.f	$4$	$16$	$8$	$18.685$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2340.2.u.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{11}q^{5}+(1+\beta _{4})q^{7}+(-\beta _{7}+\beta _{8}+\cdots)q^{11}+\cdots\)
2340.2.bp.i	$2340$	$2$	2340.bp	65.f	$4$	$28$	$14$	$18.685$		None			✓		780.2.r.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)